estimating platform market power in two-sided markets with an

Estimating Platform Market Power in Two-sided Marketswith an Application to Magazine Advertising

Minjae Song

1Simon Graduate School of BusinessUniversity of Rochester

2011 FTC Micro Conference

Song (University of Rochester) Two-sided Markets 2011 FTC Micro Conference 1 / 21

In Two-sided Markets

Two groups of agents interact through a platform.

Each group cares about the presence of agents on the other side, andthus the decisions of agents on one side affect the utility of agents onthe other side.

Platforms account for these cross-group externalities in makingstrategic decisions (e.g. setting prices).


Examples

Payment systems

Merchants and consumers interact through credit cards.

Video game systems

Game developers and game players interact through video consoles.

Advertising in newspapers/magazines/websites

Advertisers and readers interact through media platforms.


What I do in this paper

My paper brings two important features of the two-sided market intoa structural model.

Agents on each side care about the presence of agents on the otherside.Platforms charge two prices, one for each group.

I focus on cases where platforms charge fixed membership fees.

I consider two versions of the two-sided market.

Two-sided single homing: agents on both sides join one platform each.Competitive bottleneck: agents on one side join one platform butagents on the other side join multiple platforms.


I show how to estimate agents’demand (preferences) for platformsusing data on (two) membership prices, the number of agents onplatforms, and other platform attributes.

The presence of agents from the other side is an important platformattribute and this variable is an endogenous variable.

Given demand estimates, one can recover platforms’costs of servingagents and measure their markups (market power).

Price elasticity does not have a closed form because of the so-calledfeedback loop effect.There are two demand equations, one for each group, and both shouldbe used simultaneously to recover the costs.


Literature

Numerous theory papers on two-sided markets.

The most cited ones are Rochet and Tirole (JEEA 2003; RAND 2006)and Armstrong (RAND 2006).My paper is closely related to Armstrong (2006) .

Relatively few empirical papers but the number is growing fast.

Rysman (RESTUDS 2004) on the Yellow Page market - zero price forconsumers.Argentesi and Filistrucchi (JAE 2007) on the Italian newspaper market- consumers do not care about advertising.


Model 1: Two-sided single-homing

Two groups of agents, groups A and B. Each group cares about thepresence of the other group on platforms.

There are J platforms competing to attract agents from both sides.If platform j attracts sAj and s

Bj portions of the two groups, agents’

utilities are

uAij = µAj + αAsBj − λApAj + ξAj + εAij

uBij = µBj + αB sAj − λBpBj + ξBj + εBij

Consumers may choose the outside option of joining no platform andreceive zero mean utilities and an idiosyncratic shock.


Assuming εij is distributed the type I extreme value, platform j ′smarket shares are

SAj(pA , sB , ξA |Ω

)=

exp(

µAj + αAsBj − λApAj + ξAj

)1+∑Jm=1 exp

(µAm + αAsBm − λApAm + ξAm

)SBj(pA , sB , ξA |Ω

)=

exp(

µBj + αB sAj − λBpBj + ξBj

)1+∑Jm=1 exp

(µBm + αB sAm − λBpBm + ξBm

)


Model 2: Competitive bottleneck

In the competitive bottleneck model, while one group, say group A,deals with a single platform (single-homes), the other group, saygroup B, wishes to deal with multiple platforms (multi-homes).

A good example is media advertising.

For group A agents I use the same utility function used in thesingle-homing model except that I use the number of group B agentsinstead of the share.


I follow Armstrong (2006) to model group B agents’membershipdecision. I assume that she makes a decision to join one platformindependently from her decision to join another. She joins a platformas long as its net benefit is positive.Given the fixed membership fee, say pBj , a type-α

Bi agent will join

platform j ifαBi ωjn

Aj ≥ pBj .

Suppose platforms only know the distribution of αBi . Since each groupB agent is ex ante identical, a platform will charge a single price pBjand the number of group B agents joining platform j is determined by

SBj(pB , sA |Ω

)=

(1− F

(pBj

ωjnAj|θ))


Computing price elasticities

Because of the cross-group externalities

∂SAj(pA, sB , ξA |Ω

)∂pAk

6=∂sAj∂pAk

This makes elasticity computation an implicit function problem.Treating share equations as an implicit function, the elasticity can becomputed using the Implicit Function Theorem.For example, in the competitive bottleneck model,

FAj (s,p) ≡exp

(µAj + αAsBj M

B − λApAj + ξAj

)1+∑Jm=1 exp

(µAm + αAsBmMB − λApAm + ξAm

) − sAj = 0FBj (s,p) ≡

(1− G

(pBj

ωj sAj MA|θ))− sBj = 0

for j = 1, ..., J. where s are endogenous variables and p are controlvariables.


Estimation: Two-sided Single-home Model

With observed market shares treated as one of equilibria, I estimatethe following system of equations

log(sAj)− log

(sA0)

= µAj + αAsBj − λApAj + ξAj

log(sBj)− log

(sB0)

= µBj + αB sAj − λBpBj + ξBj

j = 1, ..., J .The model parameters are Ω =(

µAj , µBj ,λ

A,λB , αA, αB).

The demand-side model can be consistently estimated by the GMMwith IVs.

In addition to the price variable, the other group’s share variable is alsoan endogenous variable.

This variables is correlated with(

ξAj , ξBj

)for all js because of the

feedback loop.


Estimation: Competitive Bottleneck Model

For group A agents we have the following equation to estimate

log(sAj)− log

(sA0)= µAj + αAnBj − λApAj + ξAj

For group B agents ωj is recovered by inverting the second share

equation with a given value of θ and data on(nBj , n

Aj , p

Bj ,MB

).

Assuming that ωj is a function of platforms’non-price characteristics,we have another equation to estimate

ωjt = f(xjt |βB

).

where ωjt is computed by inverting

nBjt =

(1− F

(pBjt

ωjtnAjt|θ))

MB


Recovering marginal costs and markup

Demand estimates are used to recover platforms’costs using theprofit maximization condition. Assuming the constant marginal cost,platform j’s profit is

πj =(pAj − cAj

)sAj MA +

(pBj − cBj

)sBj MB

where MA and MB denote the total number of agents for each grouprespectively.The profit maximizing first order conditions are

∂πj

∂pAj= sAj MA +

(pAj − cAj

) ∂sAj∂pAj

MA +(pBj − cBj

) ∂sBj∂pAj

MB = 0

∂πj

∂pBj= sBj MB +

(pBj − cBj

) ∂sBj∂pBj

MB +(pAj − cAj

) ∂sAj∂pBj

MA = 0


The two marginal costs should be searched simultaneously. Thissearch process involves numerical computation of the own- andcross-price elasticities as derivatives of the implicit function for eachset of trial values.

Platform’s markup from one group is a function of its markup fromthe other group.


Empirical application

Advertising in magazines. Magazines serve readers on one side andadvertisers on the other side.

Panel data (1992 to 2010) on TV magazines in Germany.

Quarterly information on copy prices, advertising rates, advertisingpages, content pages, and circulation are collected from a non-profitpublic institution equivalent to the US Audit Bureau of Circulation.

Finding IVs from different magazine segments (Kaiser and Song, IJIO2009).


Data

There are about 10 to 15 magazines in each quarter published by 5 to7 publishers.

Each copy is sold at around 1 Euro, while one page of advertising issold at around 30,000 Euros.

The average magazine sells about 1.5 million copies in each quarter,has about 1,000 content pages and about 250 advertising pages.

The average magazine’s revenue from selling copies is about 1.5million Euros, while its advertising revenue is 7 million Euros.

It is hard to argue that the copy price covers the publishing cost. 1Euro for an over 100 page magazine seems unreasonably low.However, the low copy price is not unreasonable in the two sidedmarket.


Estimation results


Magazine (Platform) markup


Merger Analysis


Summary

My structural model has two key features of the two-sided market.

Both groups care about the presence of the other group, so thecross-group externalities are present on both sides.Platforms set different prices for each group to maximize joint profitsfrom both sides.

The empirical results show that most magazines set copy prices belowmarginal costs to increase the reader basis and make profits fromselling advertising space.

When the advertising side is ignored, the same demand estimatesimply high markups on the reader side.

Counterfactual exercises show that platform mergers do notnecessarily increase copy prices and, as a result, readers may notnecessarily be worse off in more concentrated markets.


estimating platform market power in two-sided markets with an

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